Question

jonas jogged up the hill at an average rate of \\(\frac{1}{12}\\) of a mile per minute and then walked down the hill at an average rate of \\(\frac{1}{16}\\) of a mile per minute. the round trip took him 42 minutes. what is the missing value in the table that represents the distance of the trip down the hill?

	rate (mi/min)	time (min)	distance (mi)
down the hill	\\(\frac{1}{16}\\)	\\(42 - x\\)	?

options:
\\(\frac{1}{16}x\\)
\\(\frac{1}{16}(42 - x)\\)
\\(42 - \frac{1}{16}x\\)
\\(\frac{42}{16} - x\\)

Explanation:

Step1: Recall the distance formula

The formula for distance is \( \text{Distance} = \text{Rate} \times \text{Time} \).

Step2: Identify rate and time for down the hill

For the trip down the hill, the rate is \( \frac{1}{16} \) mi/min and the time is \( 42 - x \) minutes.

Step3: Apply the distance formula

Substitute the rate and time into the distance formula: \( \text{Distance} = \frac{1}{16} \times (42 - x) \), which is \( \frac{1}{16}(42 - x) \).

Answer:

\(\frac{1}{16}(42 - x)\) (corresponding to the option with this expression)